Criticality of the exponential rate of decay for the largest nearest neighbor link in random geometric graphs  

 - Bangalore:  Department of Mathematics, Indian Institute of Science:  2006 
 - Let n points be placed independently in d−dimensional space according to the density f(x) = Ade−λxα ,λ> 0, x ∈ d, d ≥ 2. Let dn be the longest edge length for the nearest neighbor graph on these points. We show that (log n)1−1/αdn − bn converges weakly to 
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